A method for computing horizontal pressure-gradient force in an oceanic model with a nonaligned vertical coordinateстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
Web of Science
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 29 сентября 2021 г.
Аннотация:Discretization of the pressure-gradient force is a long-standing
problem in terrain-following (or $\sigma$) coordinate oceanic
modeling. When the isosurfaces of the vertical coordinate are not
aligned with either geopotential surfaces or isopycnals, the
horizontal pressure gradient consists of two large terms that tend
to cancel; the associated pressure-gradient error stems from
interference of the discretization errors of these terms. The
situation is further complicated by the non-orthogonality of the
coordinate system and by the common practice of using highly
non-uniform stretching for the vertical grids, which, unless special
precautions are taken, causes both a loss of discretization accuracy
overall and an increase in interference of the component errors.
In the present study we design a pressure-gradient algorithm which
achieves more accurate hydrostatic balance between the two components
and does not lose as much accuracy with non-uniform vertical grids at
relatively coarse resolution. This algorithm is based on the
reconstruction of the density field and the physical $z$-coordinate
as continuous functions of transformed coordinates with subsequent
analytical integration to compute the pressure-gradient force.
This approach allows not only a formally higher order of accuracy,
but it also retains and expands to high orders several important
symmetries of the original second-order scheme
(\cite{mell94,song98}), which is used as a prototype, as well as
it has build-in monotonicity constraining algorithm which prevents
appearance of spurious oscillations of polynomial interpolant, and,
consequently, insures numerical stability and robustness of the model
under the conditions of non-smooth density field and coarse grid
resolution. We further incorporate an alternative method of dealing
with compressibility of seawater which escapes pressure-gradient
errors associated with interference of the nonlinear nature of
equation of state and difficulties to achieve accurate polynomial
fits of resultant {\it in situ} density profiles.
In doing so, we generalized the monotonicity constraint to guarantee
non-negative physical stratification of the reconstructed density
profile in the case of compressible equation of state.
To verify the new method, we perform traditional idealized
(Seamount) and realistic test problems.